Step-by-step explanation:
step 1. the cube root is also to the 1/3 power
step 2. (27a^3b^7)^(1/3) = (3*3*3*a*a*a*b*b*b*b*b*b*b)^(1/3)
step 3. a third root: 3 factors in the root comes "out" of the root as 1
step 4. 3ab*b(b)^(1/3) = 3ab^2(b)^(1/3).
Separate the variables:

Separate the left side into partial fractions. We want coefficients a and b such that





So we have

Integrating both sides yields






With the initial condition y(0) = 1, we find

so that the particular solution is

It's not too hard to solve explicitly for y; notice that

Then






Answer:
d. overal size
Step-by-step explanation: